9.NA August 2018 Q.7 (B)

A ship of 8000 tonne displacement, 110 m long, floats in sea water of 1.024 t/m3 at draughts of 6 m forward and 6.3 m aft. The TPC is 16, LCB 0.6 m aft of midships, LCF 3 m aft of midships and MCT1 cm 65 tonne m, the vessel now moves into fresh water of 1.000 t/m3. Calculate the distance a mass of 50 tonne must be moved to bring the vessel to an even keel and determine the final draught.

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Given

L = 110 m
Δ = 8000 t
የsw = 1.024 t/m3
df = 6.0 m
da = 6.3 m
TPC = 16
LCB = 0.6 m aft of midship
LCF = 3.0 m aft of midship
MCT1 cm = 65 t
የfw = 1.000 t/m3
m = 50 t

To find

1. The distance a mass of 50 tonne must be moved to bring the vessel to an even keel, d
2. The final draught.

Solution

We know that  TPC = (Aw / 100) x የsw
                           16 = (Aw / 100) x 1.024
Area of water plane, Aw =  (16 x 100) / 1.024
                                       = 1562.5 m2

Change in mean draught = ((100 x Δ) / Aw) x (୧sw - ୧fw) / (୧sw x ୧fw)
                                         = (100 x 8000) / 1562.5) x (1.024 - 1.000) / (1.024 x 1.000)
                                         = 12 cm increase (As ship goes from SW to FW draught increases)

Distance from LCF to LCB = LCF - LCb ( Both aft of midship)
                                      FB = 3.0 - 0.6
                                           = 2.4 m

Shift in COB  = ((୧sw - ୧fw) / ୧sw) x FB  ------------------------------------- (1)
                      = ((1.024 - 1.000) / 1.024) x 24
              BB1 = 0.05625 m aft

Change in trim = (Δ x FB (୧sw - ୧fw)) / (MCT1 cm x ୧sw)
Substituting (1) in above equation
Change in trim = (Δ x BB1) / MCT1 cm
                        = (8000 x 0,05625) / 65
                      t = 6.92 cm by head (As ship moves from SW to FW always trim by head)

Initial trim = da - df
                = 6.3 - 6.0
                = 30 cm

New trim = Initial trim - Change in trim
               = 30 - 6.92
               = 23.08 cm

1. We know that new trim = (m x d) / MCT1 cm
                               23.08 = (50 x d) / 65
         Distance moved , d = (23.08 x 65) / 50
                                         = 30 cm

2. Change in draught Fwd = (Trim/L) x (L/2 + LCF)
                                          = (30/110) x (110/2 + 3)
                                          = 15.81 cm

    Final draught = Initial draught FWD + change in mean draught + draught change FWD
                          = 6.0 + 0.012 + 0.1581
                          = 6.278 m